Question

如图,已知CD⊥AB.(1)若△ABC为直角三角形,∠ACB=90°,求证:CD平方=AD×BD

Answer 1

证明:CD⊥AB,△ABC为直角三角形,∠ACB=90

所以：CD^2+DB^2=BC^2 1

CD^2+AD^2=AC^2 2

1+2得：2CD^2+DB^2+AD^2=BC^2+AC^2=AB^2=(AD+DB)^2=AD^2+DB^2+2AD×BD

2CD^2=2AD×BD

CD^2=AD×BD

得证.